## Algebraic Topology Seminar

Zhouli Xu

University of Chicago

Homotopy groups of spheres and the strong Kervaire invariant problem in dimension 62.

**Abstract:**Computing and understanding the homotopy groups of spheres is one of the most important and interesting questions in algebraic topology. In this talk, I will first review the known stemwise computations at the prime 2. In particular, I will briefly discuss recent work of Isaksen using motivic methods. Then I will discuss joint work with Beaudry that relates stemwise and chromatic computations. Finally, I will talk about the current status of the strong Kervaire invariant problem in dimension 62, including a sketch of the proof that twice theta five is zero.

Friday October 31, 2014 at 1:00 PM in SEO 1227